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Магистратура 2020/2021

## Байесовские методы анализа данных

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Направление: 01.04.02. Прикладная математика и информатика
Когда читается: 2-й курс, 3 модуль
Формат изучения: без онлайн-курса
Прогр. обучения: Прикладная статистика с методами сетевого анализа
Язык: английский
Кредиты: 4

### Course Syllabus

#### Abstract

This course introduces the basic theoretical and applied principles of Bayesian statistical analysis in a manner geared toward students in the social sciences. The Bayesian paradigm is particularly useful for the type of data that social scientists encounter given its recognition of the mobility of population parameters, its ability to incorporate information from prior research, and its ability to update estimates as new data are observed. #### Learning Objectives

• The goal of the course is ensure that students understand topics and principles of Bayesian approach to analyzing social science data. #### Expected Learning Outcomes

• Know strengths of the Bayesian approach for social science data and the philosophical differences between Bayesian and frequentist analyses.
• Know theoretical underpinnings of Bayesian modeling and primary estimation algorithms.
• Know Bayesian forms of the standard statistical models taught in regression and MLE courses (i.e., normal, logit/probit, Poisson, etc.)as well as a variety of measurement and multilevel models.
• Know innovative, effective methods for presenting the results from statistical investigations of empirical data.
• Be able to estimate and interpret Bayesian models from an applied perspective.
• Be able to work with major Bayesian estimation programs, especially R and SAS, so that they can use them and interpret their output.
• Be able to develop and/or foster critical reviewing skills of published empirical research using Bayesian methods.
• Be able to criticize constructively and determine existing issues with applied linear models in published work
• Have an understanding of advanced methods of Bayesian analysis.
• Have the skill to meaningfully develop an appropriate model for the research question.
• Have the skill to work with statistical software, required to analyze the data. #### Course Contents

• Introduction, Background, and Basics of Bayesian Inference
The first session will introduce the main concepts of Bayesian analysis, including its advantages over some other analytic methods.
• Review of prior topics
The session is a review of generalized linear model and some probability concepts, such as combining priors and likelihoods. All these methods serve as a foundation of Bayesian estimation.
• Priors
The session will go in much more detail about different types of priors that are used in Bayesian estimation and elicited priors for Bayesian model specification.
• Sampling methods and introduction to Bayesian analysis in R
This sessions will provide an understanding of sampling and the basics packages for Bayesian analysis in R.
• Convergence diagnostics
This session covers the R package for MCMC output convergence assessment and posterior inference.
• the Normal distribution and more on priors
This session introduces the neutral noninformative and informative conjugate beta and gamma prior distributions and their use in applied Bayesian Analysis.
• The Bayesian linear model
This session will focus creating the Bayesian linear model and discuss its application in the social science research.
• Missing data
This session will discuss application of Bayesian simulation to estimation and inference with missing data problems.
• Dichotomous variable models and IRT models
This session will cover the Bayesian estimation of a multilevel IRT model using Gibbs sampling and dichotomous variable models.
• Measurement models and identification
This session will discuss diagnostic checks for discrete data regression models using posterior predictive simulations.
• Introduction to multilevel models
This session will discuss Bayesian multilevel modeling approach to time-series cross-sectional data and other models where there is a need to cross the levels of analysis.
• Limitations of Bayesian statistics
This session look into some of the limitations that researchers face when working with Bayeisan analysis and objections that some people may have to working with Bayesian methods. #### Assessment Elements

• Mid-term take-home exam
• In-class labs and homeworks
• Final Exam #### Interim Assessment

• Interim assessment (3 module)
0.5 * Final Exam + 0.2 * In-class labs and homeworks + 0.3 * Mid-term take-home exam #### Recommended Core Bibliography

• Bolstad, W. M. (2017). Introduction to Bayesian Statistics (Vol. Third edition). Hoboken, N.J.: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1342637
• Borek Puza. (2015). Bayesian Methods for Statistical Analysis. Netherlands, Europe: ANU Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.C43E3A69
• Hahn, E. D. (2014). Bayesian Methods for Management and Business : Pragmatic Solutions for Real Problems. Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=830682
• Rossi, P. E. (2014). Bayesian Non- and Semi-parametric Methods and Applications. Princeton: Princeton University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=681619
• Yang, X.-S., & Jeliazkov, I. (2014). Bayesian Inference in the Social Sciences. Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=888972

#### Recommended Additional Bibliography

• Congdon, P. (2014). Applied Bayesian Modelling (Vol. Second edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=784135
• Hjort, N. L. (2010). Bayesian Nonparametrics. Cambridge, UK: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=312516
• Koch, K.-R. (2007). Introduction to Bayesian Statistics (Vol. 2nd, updated and enl. ed). Berlin: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=213208
• Lee, P. M. (2012). Bayesian Statistics : An Introduction (Vol. 4th ed). Chichester, West Sussex: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=463079